3.0 Polar co-ordinates of a point

Let us assume a point $P$ in the plane at a distance of $r$ from pole ($O$) at an angle $\theta $ from $X$-axis as shown in figure. The polar co-ordinates of point $P$ can be written as $P(r,\theta )$ such that $OP=r$ (radius vector) and $\angle XOP = \theta $ (vectorial angle).

$\theta $ lies between $ - \pi $ to $\pi $ i.e., $ - \pi < \theta < \pi $. If it is greater than $\pi $, then we subtract $2\pi $ from it and if it is less than $ - \pi $, then we add $2\pi $ to it.

It is also known as principal value of $P$.